The present investigation aims to find an exact solution to the problem of a free convective, viscous, radiating, chemically reacting, optically thick, non-gray, and incompressible MHD flow past an exponentially accelerated semi-infinite vertical plate in presence of a transverse magnetic field. The medium of flow is porous. Arbitrary ramped temperature and diffusion thermo effects are also considered. Rosseland approximation method is used to describe the flux that appears in the energy equation. The effects of different parameters on flow and transport characteristics are discussed with the help of suitable graphs. It is noticed that velocity field and concentration field decreases but temperature field increases with an upsurge in Schmidt number. Also, Nusselt number and skin friction rise with increasing chemical reaction parameter but lowers with increasing radiation parameter. Faster consumption of chemical substances decelerates both concentration and velocity but accelerates temperature of the fluid. An interesting outcome outcome of our investigation is that both Dufour effect and arbitrary ramped temperature diminishes fluid velocity.

The purpose of the present study is to analyze the problem of a free convective MHD flow of incompressible, electrically conducting, and viscous fluid past an impulsively started semi‐infinite moving vertical plate. The fluid is considered to be non‐gray and optically thick. The parabolic ramped temperature of the plate and thermodiffusion effect are also taken into account. A magnetic field having uniform strength is applied in the transverse direction to the fluid velocity. Solutions of dimensionless governing partial differential equations are attained on the adoption of the closed‐form Laplace transformation technique. Effects of different flow parameters on the velocity field, temperature field, concentration field, Nusselt number, skin friction, and Sherwood Number are discussed graphically. It is noticed that fluid concentration, temperature, and velocity decline considerably for ascending values of Prandtl Number. Increasing Ramped parameter hikes the Nusselt number and Sherwood Number but declines skin friction.

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The objective of the present work is to obtain an exact solution to the problem of a free convective, radiative, viscous, chemically reacting, heat absorbing, incompressible, and unsteady MHD flow past an exponentially accelerated moving vertical plate embedded in a porous medium. The fluid is assumed to be optically thick and non-gray. A magnetic field is applied in the transverse direction of the flow. Effects of arbitrary ramped temperature and thermal diffusion are also considered. Rosseland approximation method is used to describe the radiative heat flux that appears in the energy equation. Analytical solutions of the non-dimensional governing equations are obtained by adopting a closed-form of the Laplace transformation technique. The influence of various physical parameters on flow and transport characteristics is analyzed with suitable graphs. From the investigation, it is observed that increasing Soret number hikes both concentration and velocity fields. Ascending radiation parameter upsurges Nusselt number but declines Soret number.

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In this investigation, thermal diffusion and thermal radiation effects are studied on an unsteady natural convective flow of an electrically conducting fluid past an inclined vertical plate. A uniform aligned magnetic field is imposed onto the fluid or the plate. The governing PDEs are solved using the Laplace transformation technique. The effect of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number are analyzed graphically. It is observed that velocity field rises for increasing the value of the thermal-diffusion effect. Moreover, fluid concentration gets ososcillate with the effect of Prandtl number and thermal radiation parameter.